The 12th and 22nd Amendment prohibits it.
The 12th states that no person who is ineligible to run for the presidency can run for the vice presidency.
the 22nd Amendment makes Obama, Bush-43 and Bill Clinton ineligible to run for President and therefor ineligible to run for Vice President.
en.wikipedia.org
It's an odd combination of Amendments, that has only really applied to five people in our history, The three I mentioned above, Reagan and Eisenhower. It didn't apply to Jerry Ford since he had only served one partial term, and there was serious consideration to making him VP on Reagan's ticket.